Abstract not found

The moving k nearest neighbor (MkNN) query finds the k nearest neighbors of a moving query point continuously. The high potential of reducing the query processing cost as well as the large spectrum of associated applications have attracted considerable attention to this query type from the database community. This paper presents an incremental safe-region-based technique for answering MkNN queries, called the V*-Diagram. In general, a safe region is a set of points where the query point can move without changing the query answer. Traditional safe-region approaches compute a safe region based on the data objects but independent of the query location. Our approach exploits the current knowledge of the query point and the search space in addition to the data objects. As a result, the V*-Diagram has much smaller IO and computation costs than existing methods. The experimental results show that the V*-Diagram outperforms the best existing technique by two orders of magnitude.

Abstract — The popularity of location-based services and the need to do real-time processing on them has led to an interest in performing queries on transportation networks, such as finding shortest paths and finding nearest neighbors. The challenge is that these operations involve the computation of distance along a spatial network rather than “as the crow flies. ” In many applications an estimate of the distance is sufficient, which can be achieved by use of an oracle. An approximate distance oracle is proposed for spatial networks that exploits the coherence between the spatial position of vertices and the network distance between them. Using this observation, a distance oracle is introduced that is able to obtain the ε-approximate network distance between two vertices of the spatial network. The network distance between every pair of vertices in the spatial network is efficiently represented by adapting the well-separated pair technique to spatial networks. Initially, use is made of an ε-approximate distance oracle of size O ( n εd) that is capable of retrieving the approximate network distance in O(logn) time using a B-tree. The retrieval time can be theoretically reduced to O(1) time by proposing another ε-approximate distance oracle of size O ( nlogn εd) that uses a hash table. Experimental results indicate that the proposed technique is scalable and can be applied to sufficiently large road networks. A 10%-approximate oracle (ε = 0.1) on a large network yielded an average error of 0.9 % with 90 % of the answers making an error of 2 % or less and an average retrieval time of 68µ seconds. Finally, a strategy for the integration of the distance oracle into any relational database system as well as using it to perform a variety of spatial queries such as region search, k-nearest neighbor search, and spatial joins on spatial networks is discussed. I.

The advent of location-based services has led to an increased demand for performing operations on spatial networks in real time. The challenge lies in being able to cast operations on spatial networks in terms of relational operators so that they can be performed in the context of a database. A linear-sized construct termed a path oracle is introduced that compactly encodes the n2 shortest paths between every pair of vertices in a spatial network having n vertices thereby reducing each of the paths to a single tuple in a relational database and enables finding shortest paths by repeated application of a single SQL SELECT operator. The construction of the path oracle is based on the observed coherence between the spatial positions of both source and destination vertices and the shortest paths between them which facilitates the aggregation of source and destination vertices into groups that share common vertices or edges on the shortest paths between them. With the aid of the Well-Separated Pair (WSP) technique, which has been applied to spatial networks using the network distance measure, a path oracle is proposed that takes O(sdn) space, where s is empirically estimated to be around 12 for road networks, but that can retrieve an intermediate link in a shortest path in O(logn) time using a B-tree. An additional construct termed the path-distance oracle of size O(n · max(sd, 1 d ε)) (empirically (n · max(122, 2.5 2 ε))) is proposed that can retrieve an intermediate vertex as well as an ε-approximation of the network distances in O(logn) time using a B-tree. Experimental results indicate that the proposed oracles are linear in n which means that they are scalable and can enable complicated query processing scenarios on massive spatial network datasets.

Shortest path queries (SPQ) are essential in many graph analysis and mining tasks. However, answering shortest path queries on-the-fly on large graphs is costly. To online answer shortest path queries, we may materialize and index shortest paths. However, a straightforward index of all shortest paths in a graph of N vertices takes O(N 2) space. In this paper, we tackle the problem of indexing shortest paths and online answering shortest path queries. As many large real graphs are shown richly symmetric, the central idea of our approach is to use graph symmetry to reduce the index size while retaining the correctness and the efficiency of shortest path query answering. Technically, we develop a framework to index a large graph at the orbit level instead of the vertex level so that the number of breadth-first

This paper addresses the problem of monitoring the k nearest neighbors to a dynamically changing path in road networks. Given a destination where a user is going to, this new query returns the k-NN with respect to the shortest path connecting the destination and the user’s current location, and thus provides a list of nearest candidates for reference by considering the whole coming journey. We name this query the k-Path Nearest Neighbor query (k-PNN). As the user is moving and may not always follow the shortest path, the query path keeps changing. The challenge of monitoring the k-PNN for an arbitrarily moving user is to dynamically determine the update locations and then refresh the k-PNN efficiently. We propose a three-phase Best-first Network Expansion (BNE) algorithm for monitoring the k-PNN and the corresponding shortest path. In the searching phase, the BNE finds the shortest path to the destination, during which a candidate set that guarantees to include the k-PNN is generated at the same time. Then in the verification phase, a heuristic algorithm runs for examining candidates’ exact distances to the query path, and it achieves significant reduction in the number of visited nodes. The monitoring phase deals with computing update locations as well as refreshing the k-PNN in different user movements. Since determining the network distance is a costly process, an expansion tree and the candidate set are carefully maintained by the BNE algorithm, which can provide efficient update on the shortest path and the k-PNN results. Finally, we conduct extensive experiments on real road networks and show that our methods achieve satisfactory performance.

In a geographical route search, given search terms, the goal is to find an effective route that (1) starts at a given location, (2) ends at a given location, and (3) travels via geographical entities that are relevant to the given terms. A route is effective if it does not exceed a given distance limit whereas the ranking scores of the visited entities, with respect to the search terms, are maximal. This paper introduces route-search queries, suggests three semantics for such queries and deals with the problem of efficiently answering queries under the different semantics. Since the problem of answering route-search queries is a generalization of the traveling salesman problem, it is unlikely to have an efficient solution, i.e., there is no polynomial-time algorithm that solves the problem (unless P=NP). Hence, in this work we consider heuristics for the problem. Methods for effectively computing routes are presented. The methods are compared analytically and experimentally. For these methods, experiments on both synthetic and real-world data illustrate their efficiency and their effectiveness in computing a route that satisfies the constraints of a route-search query. Categories and Subject Descriptors

A spatiotemporal network is a spatial network (e.g., road network) along with the corresponding time-dependent weight (e.g., travel time) for each edge of the network. The design and analysis of policies and plans on spatiotemporal networks (e.g., path planning for location-based services) require realistic models that accurately represent the temporal behavior of such networks. In this paper, for the first time we propose a traffic modeling framework for road networks that enables 1) generating an accurate temporal model from archived temporal data collected from a spatiotemporal network (so as to be able to publish the temporal model of the spatiotemporal network without having to release the real data), and 2) augmenting any given spatial network model with a corresponding realistic temporal model custom-built for that specific spatial network (in order to be able to generate a spatiotemporal network model from a solely spatial network model). We validate the accuracy of our proposed modeling framework via experiments. We also used the proposed framework to generate the temporal model of the Los Angeles County freeway network and publish it for public use. 1.

Shortest path computation is one of the most common queries in location-based services that involve transportation networks. Motivated by scalability challenges faced in the mobile network industry, we propose adopting the wireless broadcast model for such location-dependent applications. In this model the data are continuously transmitted on the air, while clients listen to the broadcast and process their queries locally. Although spatial problems have been considered in this environment, there exists no study on shortest path queries in road networks. We develop the first framework to compute shortest paths on the air, and demonstrate the practicality and efficiency of our techniques through experiments with real road networks and actual device specifications. 1.

As geo-realistic rendering of land surfaces is becoming commonplace in geographical information systems (GIS), games and online Earth visualization platforms, a new type of k Nearest Neighbor (kNN) queries, “surface ” k Nearest Neighbor (skNN) queries, has emerged and been investigated recently, which extends the traditional kNN queries to a constrained third dimension (i.e., land surface). All existing techniques, however, assume a static environment, limiting their utility in emerging applications (e.g., Location-based Services) where objects move. In this paper, for the first time, we propose two exact methods that can continuously answer skNN queries in a highly dynamic environment which allows for arbitrary movements of data objects. The first method, inspired by the existing techniques in monitoring kNN in road networks [7] maintains an analogous counterpart of the Dijkstra Expansion Tree on land surface, called Surface Expansion Tree (SE-Tree). However, we show the concept of expansion tree for land surface does not work as SEtree suffers from intrinsic defects: it is fat and short, and hence does not improve the query efficiency. Therefore, we propose a superior approach that partitions SE-Tree into hierarchical chunks of pre-computed surface distances, called Angular Surface Index Tree (ASI-Tree). Unlike SE-tree, ASI-Tree is a well balanced thin and tall tree. With ASI-Tree, we can continuously monitor skNN queries efficiently with low CPU and I/O overheads by both speeding up the surface shortest path computations and localizing the searches. We experimentally verify the applicability and evaluate the efficiency of the proposed methods with both real world and synthetic data sets. ASI-Tree consistently and significantly outperforms SE-Tree in all cases. 1.